Question

t =5la n +6la n + 9 la 2014 este nr par,
Multumesc anticipat!

Answer 1

 

$\displaystyle\bf\\\text{Calculam ultima cifra a lui }t\\\\U(t)=U\left(5^n+6^n+9^{2014}\right)=\\\\=U\left(U\Big(5^n\Big)+U\Big(6^n\Big)+U\Big(9^{2014}\Big)\right)=\\\\=U\left(5+6+U\Big(9^{2\times1007}\Big)\right)=\\\\=U\left(5+6+U\Big(\Big(9^2\Big)^{1007}\Big)\right)=\\\\=U\left(5+6+U\Big(81^{1007}\Big)\right)=\\\\=U\left(5+6+1\right)=\\\\U(12) = \boxed{\bf2}\\\\\implies~~~t~~~\text{\bf este numar par deoarece are ultima cifra } = 2$